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Partial Fulfillment of the Requirements for the Degree of


Academic year: 2023

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In the present work, numerical models of a natural circulation test facility and its prototype (an NCBWR type pressure pipe). The Poincaré section and the Lyapunov exponent confirm the chaotic nature of the flow oscillations.

Publications from this Work


Startup Oscillations in Parallel-Channel Systems 57

List of Tables




The quality of recorded experimental data and the precision level of the available system codes, or the expected uncertainty in these predictions, are generally evaluated as satisfactory for the needs of the current reactors. The flow is susceptible to gravity-driven instabilities, especially at low-pressure low-power operating conditions (start-up) due to the high sensitivity of the flow to disturbances.

Major Objectives

However, the demand from the more extensive use of NC in the design of evolutionary and innovative water-cooled reactors requires a re-evaluation of the code properties considering the new phenomena and conditions involved. To identify an appropriate heating rate focusing on minimal void generation in the core region and faster reactor pressure.

Organization of Thesis

Conceptualize and demonstrate a ramp-up process that could make day-to-day commissioning of test facilities run smoothly and faster. In Chapter 6, numerical experiments of different heating rates are performed and a new start-up procedure is proposed and studied to illustrate a method to avoid low-pressure instabilities (flashing) that occur during NCBWR start-up.

Review of Literature

  • Introduction
  • Flow Instabilities during Startup
    • Geysering instability
    • Flashing instability
    • Geysering-induced flashing instability
    • Density wave oscillations
    • Low-pressure instabilities in parallel-channel systems
  • Experimental Facilities
  • Modeling of Startup Transients
    • Numerical codes
    • RELAP5 code
  • Startup Procedures
  • Summary

This value of the threshold pressure was also found by numerical calculation (Paniagua et al., 1999). The decrease in local pressure will cause additional steam formation, leading to a large increase in the flow rate (Jiang et al., 1995).

Numerical Model

  • Introduction
  • Code Description 1. Mathematical model
    • Numerical scheme
    • Constitutive model
  • Test Facility
  • RELAP Models
    • Nodalization schemes
    • Nodal sensitivity studies
  • Model Validation
  • Verification of NCBWR Model
  • Summary

The RELAP5 solution scheme is designed to converge based on the material Courant limit (i.e., the numerical algorithms limit the solution time step size based on the mass flow transit time through each component cell). While one simulator with its riser, drum, downcomer and feeder represents one loop (Fig. 3.2), the other loop with three simulators, three risers, a drum, a downcomer and three feeders represents the other three loops of the prototype. To determine the number of nodes in the core (or heater) and riser sections, node sensitivity studies are performed for the RELAP5 models of the test facility and prototype.

Consequently, these schemes can be selected for numerical simulations of the test facility and the prototype. It is also essential to verify the nodal sensitivity of the RELAP5 models in predicting the transient time during startup. As a verification process, the transient predictions and parametric trends (effect of pressure and flow limitations) obtained by the NCBWR model were compared with those of the NCTF model.

Analysis of Startup Oscillations

  • Introduction
  • Analysis of Startup Oscillations
    • Flow instabilities in NCTF
    • Flow instabilities in NCBWR
  • Time Series Analysis
    • Power spectrum analysis
    • Poincaré Section
    • Lyapunov exponent
  • Summary

The current transients simulated for the prototype are compared with the current transients observed in the model (NCTF). It is concluded that the low-amplitude oscillations are caused by the void pulses generated in the heater part, and the high-amplitude oscillations. In such a case, void reduction should start from the top of the heater (node ​​8), meaning that the void fraction.

Based on the length ratio, the length of the risers in the prototype will be four times the length of the model. The similarity between the nature of the startup transitions observed in the NCTF and the prototype is verified. The flickering effect is more pronounced in the prototype due to the large variation of the saturation temperature, as the length scale is 4 times larger than the model.

Startup Oscillations in Parallel-Channel Systems

  • Introduction
  • Description of Parallel-Channel Systems
    • Nodalization scheme for RELAP5 simulation
  • Results and Discussion
    • Single-channel power input
    • Double-channel power input
  • Summary and Conclusions

The hydraulic diameter of the equivalent channel is equal to the hydraulic diameter of a single channel in the prototype. Thus, there is a difference between the nature of the flow oscillations predicted in the model and the prototype, in the context of in-phase and out-of-phase behavior. In general, the main reason for the different nature of the start-up oscillations in the model and the prototype can be attributed to the lower height of the considered test facility.

The flow oscillations in the channels are found to be out of phase, with the flow pulses in Channel-2 lagging behind. Due to the out-of-phase character of the trigger pulses in the channels, the number of down-current pulses is doubled when compared to the equal-power condition where the current is in-phase. In the prototype model, the flow behavior in both channels is characterized by ignition pulses which are in phase.

Power Ramping Procedure for NCBWR

  • Introduction
  • Numerical Experiments on Reactor Heat-up Rate
    • An initial startup test
    • Simulations for various heat-up rates
  • Startup of NCBWR under Single-Phase Condition
  • Conceptualization of a New Startup Procedure
    • RELAP5 simulation procedure
    • Numerical demonstration of startup procedure
    • Point of bleed
  • Summary

Under the Case-2 strength limit condition, the system is found to generate more voids in the base section, especially in Case-2B. To keep the system in a single-phase state throughout the pressurization process, it requires control over the coolant temperature in the PHT loop. It is observed that the flow in the system is steady and there is an increase in the system pressure under single-phase heating.

It was found that the flux moves to a higher level when net vapor formation starts in the core region (20000 s). Therefore, it is also necessary to place the valves in the steam drum at a height where a single-phase condition is guaranteed. It is also necessary to place the vent valves in the steam drum at a height where a single-phase condition is always guaranteed.

Ascension to Full Power

  • Introduction
  • Power Ramping Procedure for the Test Facility
  • Prediction of Stability Boundary using RELAP5 Model
  • Experimental Demonstration of Power Ramping Procedure
  • Scale-up for NCBWR
  • Summary

The power is increased to 75% of the Type II limit for the current system pressure and core inlet subcooling. The power ramp procedure proposed in Section 7.2 was demonstrated in the test facility. When the flow became stable, an input power equal to the power at the Type-II limit for the current system pressure was obtained using the above fitting.

It can be noted that there are two main operating regions in the boost procedure used here: the initial region until transients stop (step 3) and the later region until the desired system pressure is reached (step 5). Based on the power-up procedure conceived for the test object and demonstrated experimentally, the power-up procedure is scaled up for the prototype and numerically tested. As noted in the experimental demonstration for the test facility (Section 7.4), there are two main operating regions in the power range.


98 Conclusions Chapter 8 of the starting transients observed in the test facility and in the prototype, another type of starting oscillation was found in the prototype, where there is only ignition. The existence of in-phase and out-of-phase ignition instabilities in parallel-channel systems (prototype and scale model) was investigated through the RELAP5 parallel-channel model extended from the single-channel model. The simulations were done under equal and unequal power boundary conditions and flow restrictions in the channels.

For identical initial conditions, it was concluded that the nature of the flow oscillation observed in the scale model and in the prototype is not similar, in the context of in-phase and out-of-phase behavior. Flow reversal in this context refers to the reversal of flow direction in one channel when there is a sudden increase in flow in the other channel due to flash. The consequence of the positioning of the bleeding valves used in the initiation procedure was also highlighted and it is desirable to conduct experimental studies to demonstrate these effects.

Numerical Simulation for PUMA Facility

Simulation for Startup Transients in PUMA Facility

Results and Discussion

Increasing the height of the chimney would lead to the formation of voids (flashing) in the upper part of the chimney. Figures A.5 and A.6 respectively show the discharge pipe flow rate as predicted by RELAP5 and measured during the PUMA device start-up test. In both figures, the velocity fluctuations are small during the initial transients and become large with time.

We observe a reversal of the current due to the formation of voids (in the core) and their condensation in the lower part of the riser, when the rate of condensation is higher than the rate of formation of voids. Although the trends predicted by numerical simulations are in good agreement, the need for further validation arises due to the lack of key dimensions and quantitative experimental data in the literature.

Salient Features of NCTF

  • Heater Section and riser
  • Steam Separator Drums
  • Downcomer
  • Condenser

The liquid height in both drums is scaled dimensions of the liquid height of the prototype drum. The volume of liquid in the model is scaled from the liquid volume of the prototype using the volume scale ratio as follows. The liquid volume of the one-channel boiler is 0.01349 m3. The downcomer lengths for the model are determined by the length scale ratio and the diameter is based on the scaled flow area.

The shape of the prototype head is a circular ring with a ring diameter of 17.5 m. The head dimensions for the model are determined by maintaining the volume scale and the considered head volume is 2.4 liters. The length and height of the feeders in the model are determined by the length scale, and the inner diameter of the feeder line is 26.45 mm.

Design Features of the Prototype

  • Advanced Heavy Water Reactor
  • Major Design Features
  • Reactor Physics Design
  • Heat Transport System
  • Fuel Cluster
  • Passive Safety Features of AHWR

The steam from the turbine is condensed and after cleaning the condensate and preheating it is pumped back to the steam drums and the feed water is mixed with the water separated from the steam-water mixture at 285 ºC in the steam drums. One of the most important elements of the requirements for the next generation of nuclear reactors is to incorporate passive safety features, especially for the removal of the reactor core under all operating conditions, including accident conditions, such as isolation and cooling of the containment in the event of an accident. Under normal reactor operating conditions, heat removal is achieved by natural circulation of light water coolant through the reactor core by placing steam drums at high altitude.

In the event of a Loss of Coolant Accident (LOCA), removal of reactor core decay heat and flooding of the core is achieved without operator intervention for a period of three days using ECCS accumulators and GDWP. After submersion underwater, the core cools in a long-term recirculation state. Isolation of the reactor building ventilation system is achieved through waterproofing, established due to pressure increase in the containment after LOCA and also removal of the containment heat using passive containment coolers (PCCs) with GDWP acting as a heat sink.

Flash-induced density wave oscillation in a natural circulation BWR-instability mechanism and stability maps. Experimental and analytical modeling of natural circulation and forced circulation of BWRs – thermohydraulic phenomena in the core and regional stability. Planned Experimental Studies of Natural Circulation and Stability of Boiling Water Reactors in Four Experimental Plants and First Results (NACUSP).

Nonlinear analysis for a two-channel two-phase natural circulation loop under low pressure conditions. Modeling of flash-induced instabilities in the start-up phase of natural circulation BWRs using the two-phase flow code FLOCAL. Stability of boiling water reactors with natural circulation: Part I: Description of stability model and theoretical analysis in terms of dimensionless groups.


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